Xia Rongmin, Li Xu, He Bin
Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN 55455 USA.
IEEE Trans Med Imaging. 2009 May;28(5):669-75. doi: 10.1109/TMI.2008.2008972. Epub 2009 Feb 10.
A new theory is proposed for the reconstruction of curl-free vector field, whose divergence serves as acoustic source. The theory is applied to reconstruct vector acoustic sources from the scalar acoustic signals measured on a surface enclosing the source area. It is shown that, under certain conditions, the scalar acoustic measurements can be vectorized according to the known measurement geometry and subsequently be used to reconstruct the original vector field. Theoretically, this method extends the application domain of the existing acoustic reciprocity principle from a scalar field to a vector field, indicating that the stimulating vectorial source and the transmitted acoustic pressure vector (acoustic pressure vectorized according to certain measurement geometry) are interchangeable. Computer simulation studies were conducted to evaluate the proposed theory, and the numerical results suggest that reconstruction of a vector field using the proposed theory is not sensitive to variation in the detecting distance. The present theory may be applied to magnetoacoustic tomography with magnetic induction (MAT-MI) for reconstructing current distribution from acoustic measurements. A simulation on MAT-MI shows that, compared to existing methods, the present method can give an accurate estimation on the source current distribution and a better conductivity reconstruction.
提出了一种用于重构无旋向量场的新理论，该向量场的散度用作声源。该理论应用于根据在包围源区域的表面上测量的标量声学信号来重构向量声源。结果表明，在某些条件下，标量声学测量可以根据已知的测量几何结构进行矢量化，随后用于重构原始向量场。从理论上讲，该方法将现有声学互易原理的应用领域从标量场扩展到了向量场，这表明激励向量源和传输声压向量（根据特定测量几何结构矢量化的声压）是可互换的。进行了计算机模拟研究以评估所提出的理论，数值结果表明，使用所提出的理论重构向量场对检测距离的变化不敏感。本理论可应用于磁感应磁声层析成像（MAT-MI），以便从声学测量中重构电流分布。MAT-MI的模拟表明，与现有方法相比，本方法能够对源电流分布进行准确估计，并能更好地重构电导率。
